On the complexity of algebraic number I. Expansions in integer bases
Boris Adamczewski, Yann Bugeaud
Abstract
Let b 2 be an integer. We prove that the b-adic expansion of every irrational algebraic number cannot have low complexity. Furthermore, we establish that irrational morphic numbers are transcendental, for a wide class of morphisms. In particular, irrational automatic numbers are transcendental. Our main tool is a new, combinatorial transcendence criterion.
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